5.1.3 Replacement / Module 5 Study Guide
Vergara Statway F’13
 Read the following examples:
Types of Test Results
“(true) positive”
“(true) negative”
“false positive”
“false negative”
Meaning
The test reads “positive,” and the
person does have the condition.
The test reads “negative,” and the
person does not have the condition.
The test reads “positive,” and the
person does not have the condition.
The test reads “negative,” and the
person does have the condition.
Example
A woman with HIV takes an HIV test that
confirms she is HIV-positive.
A marijuana smoker takes a drug test that
confirms that he doesn’t smoke marijuana.
A man with no cancer takes a medical test
that says he has cancer.
A pregnant woman takes a pregnancy test
that says she is not pregnant.
 Read/do:
1. In a study of the effectiveness of a particular
drug test, 10,000 randomly selected people
– both people who use drugs and those who
don’t – took one drug test each. The results
are (partially) displayed in the table.
Complete the table.
Drug user
Not a drug user
Total
Positive test
90
Negative test
Total
100
6,346
10,000
2. According to the study, what is the chance that a random copy of the drug test is positive? Is this marginal,
joint, or conditional probability? Show your work.
3. According to the study, what is the probability that a drug user will get a negative test result? Is this marginal,
joint, or conditional probability? Show your work.
4. According to the study, what is the chance that someone who doesn’t use drugs will get a positive test result? Is
this marginal, joint, or conditional probability? Show your work.
5. According to the study, what is the probability that a random person is a drug user? Is this marginal, joint, or
conditional probability? Show your work.
6. Suppose a person gets a negative test result. According to the study, what is the chance that that person
doesn’t use drugs? Is this marginal, joint, or conditional probability? Show your work.
7. According to the study, what is the probability that a random person will be a drug user and get a negative test
result? Is this marginal, joint, or conditional probability? Show your work.
8. If a person tests positive, then according to the study, what is the chance that he or she is actually a drug user?
Is this marginal, joint, or conditional probability? Show your work.
9. According to this study, how likely is it that a drug user will get a positive test result from this test? Is this
marginal, joint, or conditional probability? Show your work.
10. According to this study, what is the false-positive rate of the test? What is the false-negative rate of the test?
Use the formulas on the board. In #1-9, you already did the work for one of these. Can you find it?
11. Imagine that a group of 500,000 people are given the drug test from the study.
a. How many false positives would you expect? Show your work.
b. How many false negatives would you expect? Show your work.
12. To get hired as an employee, your sister had to take a drug test. The test is the same one as in the study for
#1-10. She received a phone call from her prospective employer saying that her drug test was positive.
According to the study, what is the probability that your sister is actually a drug user? How likely is this?
13. Suppose you are an employer who is about to hire new employees and give them the same drug test as the one
in the study for #1-10. In which two questions, above, should you be most interested? Choose from #1-10.
Why do you say this?
Hint: An employer needs to be able to make a correct interpretation of an employee’s test results without
knowing anything else about the employee.
14. If you were a drug test manufacturer (an ethical one), which
of the medical tests below would be the most desirable:
Test 1, Test 2, or Test 3? Why?
Test
Test 1
Test 2
Test 3
False-Positive
Percentage
37.4
36.4
35.7
False-Negative
Percentage
10.3
49.3
4.8
TIH 5.1.3
1. Blood donors are usually tested for HIV. The blood is screened for the safety of the blood supply and for the benefit
of the donor. One commonly used test is called ELISA. In a study of ELISA’s effectiveness, 100,000 randomly
selected blood donors were given ELISA.
a. In the study, 390 HIV-positive people got
positive test results. 92,230 HIV-free
people got negative test results. 400 of the
donors were HIV-positive altogether.
Complete the table using this information.
Positive test
Negative test
Total
HIV-free
HIV-positive
Total
b. What is the probability that an HIV-positive donor gets a positive test result? Is this marginal, joint, or
conditional probability? Show your work.
Therefore, ELISA tests positive ____ % of the time if the donor is HIV-positive.
c. What is the probability that an HIV-free donor gets a negative test result? Is this marginal, joint, or conditional
probability? Show your work.
Therefore, ELISA correctly indicates that a donor is HIV-free ____ % of the time.
d. According to the study, are most donors HIV-free? Is this marginal, joint, or conditional probability? Show your
work. Hint: What is the probability that a donor is HIV-free?
e. What is the false-negative rate for ELISA? Is this marginal, joint, or conditional probability? Show your work.
f.
What is the false-positive rate for ELISA? Is this marginal, joint, or conditional probability? Show your work.
g. According to the Centers for Disease Control (CDC) about 0.2% of college students have HIV. After a blood drive
at a college, the lab calls and tells a student that the ELISA test results indicated he has HIV.
What is the chance that the student is actually HIV positive? How likely is this? Is this marginal, joint, or
conditional probability? Show your work.
Answers (note that for credit you need to show your work properly):
a) Top row: 7370 / 92230 / 9960; Middle row: 390, 10, 400; Bottom row: 7760, 92240, 100000
b) 97.5% (cond); c) 92.6% (cond); d) 99.6% (marg) - yes; e) 0.01% (joint) f) 7.4% (joint); g) 5% (very unlikely, cond)
Module 5 Study Guide
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Vergara Statway F’13
This study guide will be provided to you during class on 11/13/13.
The solutions to the modified Lesson 5.1.3 will be given during class on 11/13/13.
The answers to the modified TIH 5.1.3 are at the bottom of the page of the modified TIH 5.1.3.
Don’t forget to do the MS Wrap-Up for Module 5 (due on the day of the quiz, 11/14/13).
1. Proportions
a. The following are equivalent to the proportion “2 out of 3”:
i.
ii.
iii.
(rounded)
iv.
(rounded)
b. Converting between fractions, decimals & percents
i. Fractions  Decimals & Percents
Example:
ii. Decimal  Percent (multiply by 100)
iii. Percent  Decimal (divide by 100)
c. If 500 people take an exam and 66% of them pass, then how many pass?
Solution: Ask yourself, 66% of 500 is what?
So 0.66 * 500 = ?
Answer: 330. Therefore, 330 people pass the exam.
2. Two-way tables
a. How to create them and fill them in
b. How to interpret them
c. How to answer questions using them
i. Examples: “how many,” proportion, percentage, probability, chance, “how likely”
d. Probability
i. Types of probabilities – know how to compute them and how to identify which you need to do
 Marginal probability
 Joint probability
 Conditional probability
ii. Showing your work with probability notation
(
)
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(
)
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 What
means in our class for two-way tables
o Answer: “A cross B” – this refers to the place where A and B “cross” in the table
e. How to find the conditional distributions for a two-way table
i. Examples: Lesson 5.1.1 #18 and TIH 5.1.1 #1D
f. Test Results
i. The meaning of true positive, true negative, false positive, and false negative
ii. How to calculate probabilities and answer questions related to test results
1. See #2c and #2d, above
2. For examples, see problems from the modified Lesson 5.1.3 and modified TIH 5.1.3